Abstract:
We present a global analysis, through traditional and a new technique, of the solar
neutrino data using total event rates of chlorine (Homestake), Gallax+GNO, SAGE,
Superkamiokande and SNO detectors for the two neutrino case. The traditional is the
grid search technique, where we calculate well known chi-square (χ
2
) function for neutrino
oscillations for a grid of the parameters ∆m2 and tan2
θ. We find our global minima in
the LMA region with ∆m2 = 2.512 · 10−5
eV2 and tan2
θ = 0.3981. We also find local
minimum χ
2 values in different regions of the parameter space. The new technique we
chose is Differential Evolution. The Differential Evolution is a population based stochastic
algorithm for optimization of real valued non-linear non-differentiable objective functions
that has become very popular during the last decade. We combined this with the traditional
grid based method for optimization of solar neutrino oscillation parameters ∆m2
and tan2
θ. We explore regions around the minima found in the global analysis using
Differential Evolution for the fine tuning of the parameters, allowing even those values of
the parameters which do not lie on any grid. We note as much as 4 times decrease in χ
2
value in the SMA region and even better goodness-of-fit as compared to our grid-based
results. All this indicates a way out of the impasse faced due to CPU limitations of the
larger grid method.
